Exact Bohr-Sommerfeld Conditions for the Quantum Periodic Benjamin-Ono Equation

  title={Exact Bohr-Sommerfeld Conditions for the Quantum Periodic Benjamin-Ono Equation},
  author={A. Moll},
  journal={Symmetry Integrability and Geometry-methods and Applications},
  • A. Moll
  • Published 2019
  • Physics, Mathematics
  • Symmetry Integrability and Geometry-methods and Applications
  • In this paper we describe the spectrum of the quantum periodic Benjamin-Ono equation in terms of the multi-phase solutions of the underlying classical system (the periodic multi-solitons). To do so, we show that the semi-classical quantization of this system given by Abanov-Wiegmann is exact and equivalent to the geometric quantization by Nazarov-Sklyanin. First, for the Liouville integrable subsystems defined from the multi-phase solutions, we use a result of Gerard-Kappeler to prove that if… CONTINUE READING
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